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Dynamic power management (DPM) techniques are crucial in minimizing the overall energy consumption in real-time embedded systems. The timing constraints of real-time applications and non-trivial time/energy transition overheads introduce significant challenges, as the device sleep intervals should be longer than a minimum threshold (called the break-even time) to ensure energy-efficiency. In this paper, we present a novel approach to the real-time DPM problem by explicitly enforcing long device sleep intervals for different devices, called device forbidden regions. We focus on the application of our technique to task systems with rate-monotonic priorities, and develop our algorithm DFR-RMS. Our solution includes a static component where the duration and frequency of forbidden regions are determined through the extended time-demand analysis to preserve the temporal correctness of all the tasks, while enhancing the energy savings. Then, we present a sophisticated on-line component which interacts with existing prediction-based DPM schemes to realize the full potential of device forbidden regions. Further, our scheme can be used with or without dynamic voltage scaling (DVS). Our experimental evaluation hints that significant energy gains can be obtained, when compared to the existing prediction-based techniques. Another contribution of this research effort is to show that the general problem of generating feasible schedules for preemptive periodic real-time tasks where all device sleep intervals are longer than the device break-even times is NP-hard in the strong sense.